initCholReg_spam

Computes the Cholesky decomposition for the quadratic term in the (Gaussian) posterior
of the TVP regression coefficients. The sparsity pattern will not change during the
MCMC, so we can save computation time by computing this up front.

Provides efficient Markov chain Monte Carlo (MCMC) algorithms for
dynamic shrinkage processes, which extend global-local shrinkage priors to
the time series setting by allowing shrinkage to depend on its own past.
These priors yield locally adaptive estimates, useful for time series and
regression functions with irregular features. The package includes full MCMC
implementations for trend filtering using dynamic shrinkage on signal differences,
producing locally constant or linear fits with adaptive credible bands.
Also included are models with static shrinkage and normal-inverse-Gamma priors for comparison.
Additional tools cover dynamic regression with time-varying coefficients and
B-spline models with shrinkage on basis differences, allowing for flexible
curve-fitting with unequally spaced data. Some support for heteroscedastic errors,
outlier detection, and change point estimation.
Methods in this package are described in Kowal et al. (2019) <doi:10.1111/rssb.12325>,
Wu et al. (2024) <doi:10.1080/07350015.2024.2362269>, Schafer and Matteson (2024)
<doi:10.1080/00401706.2024.2407316>, and Cho and Matteson (2024) <doi:10.48550/arXiv.2408.11315>.

Toryn Schafer

Dynamic Shrinkage Process and Change Point Detection

Daniel R. Kowal

Haoxuan Wu

Jason B. Cho

David S. Matteson

initCholReg_spam function

<dl><dt>obs_sigma_t2</dt>
<dd>the <code>T x 1</code> vector of observation error variances</dd>
<dt>evol_sigma_t2</dt>
<dd>the <code>T x p</code> matrix of evolution error variances</dd>
<dt>XtX</dt>
<dd>the <code>Tp x Tp</code> matrix of X'X (one-time cost; see ?build_XtX)</dd>
<dt>D</dt>
<dd>the degree of differencing (one or two)</dd></dl>

Arguments

Compute initial Cholesky decomposition for TVP Regression — initCholReg_spam

<dl>

<dt>obs_sigma_t2</dt>
<dd>the <code>T x 1</code> vector of observation error variances</dd>


<dt>evol_sigma_t2</dt>
<dd>the <code>T x p</code> matrix of evolution error variances</dd>


<dt>XtX</dt>
<dd>the <code>Tp x Tp</code> matrix of X'X (one-time cost; see ?build_XtX)</dd>


<dt>D</dt>
<dd>the degree of differencing (one or two)</dd>

</dl>

initCholReg_spam: Compute initial Cholesky decomposition for TVP Regression

Description

Usage

Arguments